Question

Given below are two statements, one is labelled as Assertion (A) and other one labelled as Reason (R).
Assertion (A): Mie scattering depends on the size of the scatterers in relation to the wavelength of radiation being scattered.
Reason (R): Approximate particle size of Mie scatterer is 0.1 to 10 $\mu$m.
In light of the above statements, choose the correct answer from the options given below.

• A. Both (A) and (R) are true and (R) is the correct explanation of (A).
• B. Both (A) and (R) are true but (R) is NOT the correct explanation of (A).
• C. (A) is true but (R) is false.
• D. (A) is false but (R) is true.

Hint:

Scattering comparison based on particle size (\(d\)) relative to wavelength (\(\lambda\)):
- Rayleigh: \(d \ll \lambda\) (gas molecules, causes blue sky).
- Mie: \(d \approx \lambda\) (dust, smoke, pollen, \(0.1\text{ to }10\text{ }\mu\text{m}\)).
- Non-selective: \(d \gg \lambda\) (water droplets in clouds, causes white clouds).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
When electromagnetic radiation travels through the Earth's atmosphere, it interacts with gas molecules, dust, and aerosols, causing the radiation to scatter in different directions.
The type of scattering depends on the ratio of the atmospheric particle diameter (\(d\)) to the wavelength of the incident radiation (\(\lambda\)).

Step 2: Detailed Explanation:
Let us analyze both statements and their relationship:
- Assertion (A): Atmospheric scattering is classified into three types based on the relative size of the scattering particles compared to the wavelength of the light:
1. Rayleigh scattering: Occurs when particle diameters are much smaller than the wavelength (\(d \ll \lambda\)), such as air molecules scattering blue light.
2. Mie scattering: Occurs when the size of the atmospheric particles is approximately equal to the wavelength of the light being scattered (\(d \approx \lambda\)).
3. Non-selective scattering: Occurs when particle diameters are much larger than the wavelength (\(d \gg \lambda\)), such as water droplets in clouds scattering all wavelengths of visible light equally.
Therefore, Mie scattering depends directly on the size of the scatterers relative to the wavelength of the incident radiation, making Assertion (A) correct.
- Reason (R): Typical Mie scatterers in the atmosphere include smoke, fine dust, pollen, and microscopic water droplets.
These particles have diameters ranging from approximately \(0.1\text{ }\mu\text{m}\) to \(10\text{ }\mu\text{m}\).
Since visible, near-infrared, and short-wave infrared wavelengths fall within this same range (\(0.4\text{ to }3.0\text{ }\mu\text{m}\)), these wavelengths undergo Mie scattering when they interact with these particles.
Therefore, Reason (R) is correct, and it serves as the correct physical explanation for Assertion (A) by defining the specific particle sizes that match the wavelengths of the scattered radiation.

Step 2: Final Answer:
Both (A) and (R) are true and (R) is the correct explanation of (A).